Posts Tagged ‘ Risk Measures ’

Simulating Multiple Asset Paths in R

November 5, 2012
By
Simulating Multiple Asset Paths in R

I recently came across the Optimal Rebalancing Strategy Using Dynamic Programming for Institutional Portfolios by W. Sun, A. Fan, L. Chen, T. Schouwenaars, M. Albota paper that examines the cost of different rebablancing methods. For example, one might use calendar rebalancing: i.e. rebalance every month / quarter / year. Or one might use threshold rebalancing:

Read more »

Volatility Quantiles

June 4, 2012
By
Volatility Quantiles

Today I want to examine the performance of stocks in the S&P 500 grouped into Quantiles based on one year historical Volatility. The idea is very simple: each week we will form Volatility Quantiles portfolios by grouping stocks in the S&P 500 into Quantiles using one year historical Volatility. Next we will backtest each portfolio

Read more »

Gini Efficient Frontier

March 23, 2012
By
Gini Efficient Frontier

David Varadi have recently wrote two posts about Gini Coefficient: I Dream of Gini, and Mean-Gini Optimization. I want to show how to use Gini risk measure to construct efficient frontier and compare it with alternative risk measures I discussed previously. I will use Gini mean difference risk measure – the mean of the difference

Read more »

Backtesting Asset Allocation portfolios

March 18, 2012
By
Backtesting Asset Allocation portfolios

In the last post, Portfolio Optimization: Specify constraints with GNU MathProg language, Paolo and MC raised a question: “How would you construct an equal risk contribution portfolio?” Unfortunately, this problem cannot be expressed as a Linear or Quadratic Programming problem. The outline for this post: I will show how Equal Risk Contribution portfolio can be

Read more »

Portfolio Optimization – Why do we need a Risk Model

February 26, 2012
By
Portfolio Optimization – Why do we need a Risk Model

In the last post, Multiple Factor Model – Building Risk Model, I have shown how to build a multiple factor risk model. In this post I want to explain why do we need a risk model and how it is used during portfolio construction process. The covariance matrix is used during the mean-variance portfolio optimization

Read more »

Multiple Factor Model – Building Risk Model

February 20, 2012
By
Multiple Factor Model – Building Risk Model

This is the fourth post in the series about Multiple Factor Models. I will build on the code presented in the prior post, Multiple Factor Model – Building CSFB Factors, and I will show how to build a multiple factor risk model. For an example of the multiple factor risk models, please read following references:

Read more »

Backtesting Minimum Variance portfolios

December 12, 2011
By
Backtesting Minimum Variance portfolios

I want to show how to combine various risk measures I discussed while writing the series of posts about Asset Allocation with backtesting library in the Systematic Investor Toolbox. I will use Minimum Variance portfolio as an example for this post. I recommend reading a good discussion about Minimum Variance portfolios at Minimum Variance Sector

Read more »

Maximizing Omega Ratio

November 3, 2011
By
Maximizing Omega Ratio

The Omega Ratio was introduced by Keating and Shadwick in 2002. It measures the ratio of average portfolio wins over average portfolio losses for a given target return L. Let x.i, i= 1,…,n be weights of instruments in the portfolio. We suppose that j= 1,…,T scenarios of returns with equal probabilities are available. I will

Read more »

Minimizing Downside Risk

November 1, 2011
By
Minimizing Downside Risk

In the Maximum Loss and Mean-Absolute Deviation risk measures, and Expected shortfall (CVaR) and Conditional Drawdown at Risk (CDaR) posts I started the discussion about alternative risk measures we can use to construct efficient frontier. Another alternative risk measure I want to discuss is Downside Risk. In the traditional mean-variance optimization both returns above and

Read more »

The Most Diversified or The Least Correlated Efficient Frontier

October 27, 2011
By
The Most Diversified or The Least Correlated Efficient Frontier

The “Minimum Correlation Algorithm” is a term I stumbled at the CSS Analytics blog. This is an Interesting Risk Measure that in my interpretation means: minimizing Average Portfolio Correlation with each Asset Class for a given level of return. One might try to use Correlation instead of Covariance matrix in mean-variance optimization, but this approach,

Read more »